Real-rooted atlas

Proof step

Geometric basis map (elementary)

Image under a basis map u^k -> P_k A013611

Concludes
basis_map_A013611 of Triangle T(n, k) read by rows: T(n, k) = Sum_{j=0..n} binomial(j, n-k) * |Stirling1(n, n-j)|.
Premises
Theorem
polytool ?
Checked
polytool replayed · Lean not attempted
Technical details
Step id
e-3d3e7193ca830199 · JSON
Operation
Image under a basis map u^k -> P_k
{
  "map": "A013611",
  "operation": "basis_map"
}
Claims
{
  "claim": "real_rooted",
  "from_index": 0,
  "region": {
    "upper": {
      "closed": true,
      "value": "0"
    }
  }
}
Certificate
basis_map, SHA-256 a40353b70873038da0c45372bdc6e810da33bb2f0db92017cb4831803ddc56ad, 7,661 bytes (1,704 compressed); download
polytool replayed the certificate when the step was written.
Cited by